Rewrite as a simplified fraction. ${1.\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 16.6666...\\ 1x &= 1.6666...\end{align*}}$ Subtracting the two equations, we have: ${9x = 15}$ ${x = \dfrac{15}{9}} $ ${x = \dfrac{5}{3}} \text{or} {1 \dfrac{2}{3}}$